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Omni-MATH / Rachel has the number 1000 in her hands. When she puts the number x in her left pocket, the number changes to x+1. When she puts the number x in her right pocket, the number change…

Problem

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problem

Rachel has the number 1000 in her hands. When she puts the number xx in her left pocket, the number changes to x+1x+1. When she puts the number xx in her right pocket, the number changes to x−1x^{-1}. Each minute, she flips a fair coin. If it lands heads, she puts the number into her left pocket, and if it lands tails, she puts it into her right pocket. She then takes the new number out of her pocket. If the expected value of the number in Rachel's hands after eight minutes is EE, then compute ⌊E10⌋\left\lfloor\frac{E}{10}\right\rfloor.
Plain-text mathematical notation (without MathML)
Rachel has the number 1000 in her hands. When she puts the number x in her left pocket, the number changes to x+1. When she puts the number x in her right pocket, the number changes to x^(−1). Each minute, she flips a fair coin. If it lands heads, she puts the number into her left pocket, and if it lands tails, she puts it into her right pocket. She then takes the new number out of her pocket. If the expected value of the number in Rachel's hands after eight minutes is E, then compute ⌊(E)/(10)⌋.
Original LaTeX notation
Rachel has the number 1000 in her hands. When she puts the number $x$ in her left pocket, the number changes to $x+1$. When she puts the number $x$ in her right pocket, the number changes to $x^{-1}$. Each minute, she flips a fair coin. If it lands heads, she puts the number into her left pocket, and if it lands tails, she puts it into her right pocket. She then takes the new number out of her pocket. If the expected value of the number in Rachel's hands after eight minutes is $E$, then compute $\left\lfloor\frac{E}{10}\right\rfloor$.

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Source and history

task_id
1e428542-6713-5b3a-a1c0-6c119976b1e4
task_key
test--1e428542-6713-5b3a-a1c0-6c119976b1e4
task_revision_id
1
config / split
/ test

Official source

initial import